Spherical Trigonometry, for the Use of Colleges and Schools: With Numerous Examples |
From inside the book
Results 1-5 of 10
Page
... Plane Trigonometry , to which it is intended as a sequel ; it contains all the propositions usually included under ... Geometry published in the Library of Useful Knowledge . The examples have been chiefly selected from the University ...
... Plane Trigonometry , to which it is intended as a sequel ; it contains all the propositions usually included under ... Geometry published in the Library of Useful Knowledge . The examples have been chiefly selected from the University ...
Page
... Plane and Spherical Trigonometry ; so as to include an account of the properties in Spherical Trigonometry which are analogous to those of the Nine Points Circle in Plane Geometry . The mode of investigation is more elementary than ...
... Plane and Spherical Trigonometry ; so as to include an account of the properties in Spherical Trigonometry which are analogous to those of the Nine Points Circle in Plane Geometry . The mode of investigation is more elementary than ...
Page
... Geometry IV . Relations between the Trigonometrical Functions of the Sides and the Angles of a Spherical Triangle V ... Plane and Spherical Trigo- nometry 96 XIII . Polyhedrons 114 XIV . Arcs drawn to fixed points on the Surface of a ...
... Geometry IV . Relations between the Trigonometrical Functions of the Sides and the Angles of a Spherical Triangle V ... Plane and Spherical Trigo- nometry 96 XIII . Polyhedrons 114 XIV . Arcs drawn to fixed points on the Surface of a ...
Page 12
... difference of the other two . 30. The sum of the three sides of a spherical triangle is less than the circumference of a great circle . ( See the figure of Art . 18. ) For the sum of the three plane angles which form 12 SPHERICAL GEOMETRY .
... difference of the other two . 30. The sum of the three sides of a spherical triangle is less than the circumference of a great circle . ( See the figure of Art . 18. ) For the sum of the three plane angles which form 12 SPHERICAL GEOMETRY .
Page 13
With Numerous Examples Isaac Todhunter. For the sum of the three plane angles which form the solid angle at O is less than four right angles ( Euclid , XI . 21 ) ; therefore therefore , AB + BC CA + is less than 2π , OA OA ... GEOMETRY . 13.
With Numerous Examples Isaac Todhunter. For the sum of the three plane angles which form the solid angle at O is less than four right angles ( Euclid , XI . 21 ) ; therefore therefore , AB + BC CA + is less than 2π , OA OA ... GEOMETRY . 13.
Other editions - View all
Common terms and phrases
ambiguity angular points approximately arcs drawn arcs which join bisecting centre circular measure cos a cos cos² cos³ cosb cosines Crown 8vo deduce denote equation equilateral escribed circles example expression faces fixed points formulæ formulæ of Art greater Hence inscribed Legendre's Theorem less Let ABC lune meet middle point Napier's analogies Napier's Rules obtain octahedron opposite angle opposite sides parallelepiped Plane Geometry plane triangle Plane Trigonometry polar triangle pole polygon position preceding Article primitive triangle quadrant r₁ regular polyhedron respectively result right angles right-angled triangles shew shewn Similarly sin b cos sin b sin sin² sin³ sine small circle described solid angles solution sphere spherical excess spherical triangle Spherical Trigonometry ß³ straight lines subtended suppose surface tangent tetrahedron Trigono
Popular passages
Page 28 - If two triangles have two sides of the one equal to two sides of the...
Page 49 - B . sin c = sin b . sin C cos a = cos b . cos c + sin b . sin c cos b = cos a . cos c + sin a . sin c cos A cos B cos c = cos a . cos b + sin a . sin b . cos C ..2), cotg b . sin c = cos G.
Page 12 - Any two sides of a spherical triangle are together greater than the third side.
Page 19 - Thus the sines of the angles of a spherical triangle are proportional to the sines of the opposite sides.
Page 30 - From this proposition, it is obvious that if one angle of a triangle be equal to the sum of the other two angles, that angle is a right angle, as is shewn in Euc.
Page 1 - A sphere is a solid bounded by a surface, every point of which is equally distant from a fixed point called the centre.
Page 62 - A circle which touches one side of a triangle and the other two sides produced, is called an escribed circle of the triangle.
Page 15 - If one angle of a spherical triangle be greater than another, the side opposite the greater angle is greater than the side opposite the less angle.